In "multi-compartment electrodialysis" ("ED") many ion exchange ("IX") membranes are arranged between a single pair of electrodes. The membranes are of two types: cation exchange membranes ("CXM") and anion exchange membranes ("AXM"). The CXM are relatively permeable to positively charged, low molecular weight ions and relatively impermeable to negatively charged ions and to high molecular weight neutral molecules whereas AXM are relatively permeable to negatively charged, low molecular weight ions and relatively impermeable to positively charged ions (and also to high molecular weight neutral molecules). The CXM and AXM alternate between the above mentioned single pair of electrodes. Spaces are left between the membranes through which are passed aqueous solutions. When a direct electric current is passed between the electrodes, positively charged ions in the solutions ("cations", generally metallic ions such as sodium, magnesium, calcium) are pulled toward the negatively charged electrode ("cathode"). Small cations easily pass through CXM but not through AXM. Simultaneously negatively charged ions in the solutions ("anions", generally non-metallic ions such as chloride, nitrate, bicarbonate, fluoride, sulfate) are pulled toward the positively charged electrode ("anode"). Small anions easily pass through AXM but not through CXM. As a result, spaces which are on the cathode side of AXM (on the anode side of CXM) are at least partially deionized by the direct electric current. Such spaces are generally called "diluting" spaces. Spaces which are on the anode side of AXM (on the cathode side of CXM) accumulate the ions removed from the diluting spaces. Such enriched spaces are generally called "concentrating" spaces. ED is made continuous by flowing the solutions between the membranes. In such case the spaces must be enclosed by frames ("spacers") to prevent mixing of the solution in the diluting spaces ("dilute solution" or "dilute") with that in the concentrating spaces ("concentrate solution" or "concentrate"). Holes are provided in the membranes registering with similar holes in the frames thereby forming (internal) manifolds to distribute the solutions to the appropriate spaces (cavities in the frames) and to collect separately the dilute and concentrate solutions. Channels in the frames which enclose the concentrating spaces connect such spaces with the concentrate solution manifolds, and channels in the frames which enclose the diluting spaces connect the latter spaces with the dilute solution manifolds. The channels and/or frames are arranged (designed) so that the flows of solutions are uniform over the surfaces of the membranes. Regions in the diluting spaces in which the solution velocity is lower than average will be more highly deionized than the average extent of deionization. Regions in the concentrating spaces in which solution velocity is lower than average will be more enriched (concentrated) than average. If the solution being deionized contains sparingly soluble salts (such as calcium sulfate or calcium bicarbonate) then such salts may precipitate on or in those membrane surfaces in contact with regions in the concentrating spaces having velocities lower than average.
Roughly 95% of the direct electric current passing through CXM is carried by cations passing from the diluting spaces to the concentrating spaces (the remaining 5% carried by anions passing through the CXM from the concentrating spaces to the diluting spaces). The fraction of the current carried by a given ion is referred to as the "transport number". In the above case the transport number of CXM for cations is approximately 0.95. Similarly the transport number of AXM for anions is approximately 0.95 (and the transport number for cations passing through the AXM from the concentrating spaces to the diluting spaces is about 0.05). In aqueous solutions of mineral salts, the transport number for both anions and cations is roughly 0.5, that is roughly half the current is carried by anions and half by cations. For example, in the case of aqueous solutions of sodium chloride, 40% of the electric current is carried by positively charged sodium ions (i.e. transport number 0.4) and 60% by negatively charged chloride ions. Hence while 95% of the electric current is carried by sodium ions through a CXM (in the case of sodium chloride solutions) only 40% of the current is carried to the CXM by sodium ions. At the interface between the dilute solution and the CXM there is therefore a deficit in sodium ion transport equivalent to 95-40=55% of the current. Such deficit leads rapidly (in roughly one second) to a reduction in the sodium chloride concentration at the above mentioned interface to such a value that the missing 55% of the current is brought to the interface by diffusion. A mass balance leads to ##EQU1## where "i" is the current density in amperes per cm.sup.2, t is the transport number for sodium ions in the CXM (0.95), t is the transport number for sodium ions in aqueous solutions of sodium chloride (0.40), D is the diffusion coefficient (in cm.sup.2 per second) for sodium chloride (not sodium ions) in aqueous solution (1.36.times.10.sup.-5 at 18.degree. C., 64.degree. F.), F is the quantity of current required to transport one gram-equivalent of any ion at a transport number of exactly 1 (96, 480 amperes per gram-equivalent per second, called Faraday's constant), ##EQU2## is the concentration gradient built up because of the deficit in electrical transport of sodium ions, C.sub.m is the concentration (in gram-equivalents per cm.sup.3) at the above mentioned interfaces, .delta. is the distance (in cm) from the interface to the plane in the aqueous solution (parallel to the membrane) where the concentration is C. If the flow is in the streamline (laminar flow) region then .delta. is half the distance from the CXM through the diluting space to the AXM. Even when the general flow is not in the streamline region, a layer of solution adjacent to the CXM membrane remains in the streamline region, in which case .delta. is the thickness of such layer and C is the concentration outside such layer, essentially the bulk concentration. The above mass balance equation may be rearranged to: ##EQU3## where ##EQU4## it is the quantity of sodium ions (in gram-equivalents per second per cm.sup.2) transported by a current having a density of i amperes per cm.sup.2. Inspection of this equation shows ##EQU5## increases as D (the specific rate of diffusion) increases. D is inversely proportional to the viscosity of the solution and directly proportional to the absolute temperature and therefore in the case of aqueous solutions increases at a compound rate of about 2.25% per .degree.C. Therefore there is an advantage to operating at elevated temperatures. The electrical energy consumption (in watt-seconds per gram-equivalent of sodium ion removed through a CXM) is IRF/t where (as mentioned above) i is in amperes per cm.sup.2, F is the quantity of current required to remove 1 gram-equivalent per second of sodium ion through a CXM having a transport number of exactly 1 (96,480 amperes per gram-equivalent per second), t is the actual transport number of the CXM and R is the sum of the electrical resistances per cm.sup.2 of one CXM, one AXM, one diluting space and one concentrating space. R decreases at a compound rate of about 2% per .degree.C. (i.e. the same rate at which the viscosity of water decreases), increasing the importance of operating at elevated temperatures. Almost all of the electrical energy consumption goes into heating the dilute and concentrate solutions. Therefore it is often practical to warm those solutions by recuperative heat exchangers, transferring heat from the effluent solutions to the influent solutions. If the electrical energy used in ED is generated locally (e.g. by a diesel electric generator or a packaged stream electric generator) then the waste heat may be used to elevate the temperatures of the influent solutions at least enough to make recuperative heat exchange practical.
Further inspection of the above equation (2) shows that it/F increases as t/(t-t) increases as illustrated in the following table:
______________________________________ Relative Relative Relative t t/(t - t) it/F i Energy ______________________________________ 0.95 1.73 1.00 1.00 1.00 0.85 1.89 1.09 1.22 1.37 0.75 2.14 1.24 1.57 1.99 0.65 2.60 1.51 2.20 3.22 0.55 3.67 2.12 3.67 6.33 0.45 9.00 5.21 11.00 23.2 ______________________________________
The third column in the above table ("Relative i t/F") is the relative amount of sodium ion removed per cm.sup.2 per second, other things on the right hand side of above equation (2) being equal (i.e. C, C.sub.m, D (which is a constant for sodium chloride dependent only on temperature) and .delta.). The fourth column ("Relative i") is the relative current density (in amperes per cm.sup.2) corresponding to t and it/F while the last column ("Relative Energy") is the relative energy (watt-seconds per gram-equivalent sodium ion removed) other things on the right hand side of equation (2) being equal. It will be seen that, except for the case where very few gram-equivalents of sodium must be removed, it may not be practical to increase it/F (the rate of removal of sodium ion) by increasing t/(t-t). (Water having 584 ppm sodium chloride has 10 gram-equivalents of sodium per cubic meter (1 cubic meter=1 metric tonne=264 U.S. gallons)).
Inspection of equation (2) also shows that it/F (the rate of removal of sodium ion in gram-equivalents per cm.sup.2 per second) increases as .delta. decreases. (.delta. is the distance (in cm) from the interface between the CXM and the solution to the plane in the aqueous solution (parallel to the membrane) where the concentration is C). In many respects, .delta. is only an adjustable constant which correlates the data and cannot otherwise be measured. It correlates with a similar ".delta." (but is not the same as) derived from liquid momentum transfer to the membrane (viscosity loss due to friction at the membrane). It also correlates with (but is not the same as) a similar .delta. derived from heat transfer from solution to the membrane. .delta. for diffusion of sodium chloride to a membrane, is about 0.05 cm for non flowing solutions (apparently due to gravitational convection caused by density differences, in turn caused by concentration and temperature differences). If the distance from the CXM through the dilute solution to the AXM is 0.01 cm then, even when the flow of dilute solution is in the streamline (laminar flow) region, .delta. will be 0.005 cm. (Such CXM/AXM separation seems never to have been tried; no doubt there are interesting engineering problems associated with such small separation but there are no fundamental reasons why such is not possible). Values of .delta. of 0.005 cm are achieved in tortuous path spacers in use commercially from 1954. Such spacers have thicknesses of 0.1 cm (the distance from the CXM to the AXM is 0.1 cm) and have rectangular barriers 0.05 cm thick spaced about 1.4 cm from each other. The barriers alternate from the CXM side to the AXM side. Other spacers are in use or have been in use which use no barriers at all or use barriers provided by screens, expanded plastic sheet or perforated and corrugated plastic sheet. Non-woven screens having a close spacing between strands and oriented to make the flow direction change very frequently by 90.degree. angles, easily result in .delta. of about 0.001 cm (and therefore in much increased it/F, other things in equation (2) being equal). Spacers may be rated by the pressure loss per linear cm to achieve a certain .delta.. on such basis the tortuous path spacers, referred to above, are quite inefficient. This is apparently due to the relatively large pressure losses at the trailing edge of the rectangular barriers, the turbulence resulting therefrom being rapidly damped out before the next barrier in the flow path is reached. The non-woven screens referred to above (oriented to cause frequent 90.degree. changes in flow direction) are much more efficient in terms of it/F achieved for a given pressure loss per cm flow path length. Most efficient seem to be spacers without any barriers operating in the turbulent flow regime for which .delta. of 0.0005 cm seems readily achievable. .delta. is apparently insensitive to temperature.
Additional inspection of equation (2) shows that it/F increases as C.sub.m (the concentration at the membrane-solution interface) decreases. C.sub.m can, in principle, never be less than zero. When C.sub.m is so small that it can be neglected in terms of C for practical purposes, then equation (2) may be written ##EQU6## it/FC is then said to have its "limiting value". Equation (3) points out that when C.sub.m may be neglected in terms of C then it/FC is determined only by D (the diffusion coefficient of sodium chloride), t (the transport number of sodium ions in the CXM), t (the transport number of sodium ions in solution) and .delta. (the thickness of the laminar flow layer adjacent to the CXM or half the distance to the AXM, whichever is smaller). When D, t, t and .delta. are constant, i (said in this case to be the "limiting i") is proportional to C (the concentration of sodium chloride at the mid point between the CXM and the AXM in the diluting space). It is apparent experimentally that C.sub.m never actually becomes zero. The concentration gradient across the laminar flow layer adjacent to the CXM is constant, i.e. the concentration of sodium chloride decreases linearly with distance to the CXM through such layer. As a result, when C.sub.m may be neglected compared to C, there is a (non-linear) electrical potential drop of a few tenths of a volt across the laminar flow layer. The on-set of such a potential drop is most easily seen by plotting E/i versus 1/i (where E/i is the apparent resistance of a cell pair (one diluting space, one CXM, one concentrating space and one AXM)). Such a technique was first used by Cowan and Brown. A plot of E/i versus 1/i shown in FIG. 1A.
The i corresponding to the inflection point (1) is generally referred to as the "limiting current density" and may be regarded as the current density at which C.sub.m first becomes negligible compared to C. C.sub.m actually reaches its steady-state value (close to but not at zero) at inflection point (2). FIG. 1A shows that as i increases (1/i decreases), it reaches a "plateau" at point (1) where it is essentially constant while E (and R) increase (E by a few tenths of a volt as mentioned above). As i increases beyond inflection point (2) (1/i decreases below such point) the current continues to increase but at a voltage level higher by a few tenths of a volt. At such latter current, the situation in the laminar flow layer may be regarded as an essentially constant concentration gradient (C.sub.m, the concentration at the interface between the CXM and the diluting solution being close to zero) and therefore resulting in an essentially constant electrical resistance. (The derivative d E/ d i will be essentially constant). The voltage difference between a 1 normal (1 gram equivalent per liter) solution of hydroxide ion and a 1 normal solution of hydrogen ion at room temperature is about 0.8 volts. Therefore as the voltage difference at the CXM-dilute solution interface approaches a few tenths of a volt, hydrogen ions from the dissociation of water will accompany the sodium ions passing from the diluting solution into the concentrating solution, an equal number of hydroxide ions passing from the interface into the diluting solution. The concentrating solution will then become slightly acidic and the diluting solution slightly alkaline. However the rate at which water can dissociate is relatively small compared to the rate at which sodium ions are typically transferred and therefore the changes in acidity and alkalinity respectively are quite small.
The above discussion seems to have covered all that can be learned from equation (2). However i is the current density locally per cm.sup.2 of membrane area. If the membrane is planar and smooth then the local area is that which may be measured with a straight edge. (It is possible that, if a membrane which appears flat and smooth to the "naked eye", were looked at by an electron microscope it would appear rough on a scale of a micrometer or less. However if such roughness is small compared to .delta., then with respect to equation (2) the membrane is still "flat and smooth"). If the membrane has a surface texture the roughness of which is comparable with or larger than .delta., then the area which must be used to calculate i is not the straight edge area but the "actual area" including such roughness. (Such roughness may also contribute to converting pressure loss into decreased .delta.). The "actual area" of a CXM may be increased also by filling the diluting space between the CXM and the AXM with cation exchange beads ("CXB"). The increase in area may be easily calculated from the diameter of such beads. Such filling can increase the limiting value of it/FC by an order of magnitude or more. (The limiting value of it/FC is that value at which for practical purposes, C.sub.m (the concentration at the interface between the CXM (and the CXB)) becomes negligible compared to C).
The above discussion of phenomena taking place at the interface between an ion exchange membrane and a dilute solution was confined to CXM. The phenomena at an AXM are quite similar, with two exceptions. The first exception arises because the transport number of chloride ions in aqueous solution is 0.6 whereas (necessarily) the transport number of sodium ions is 0.4. Using equation (2), ##EQU7## where in this case i t/F is the rate of transfer of chloride ions through an AXM, D (as before) is the diffusion constant of sodium chloride in aqueous solution, t is 0.6, the following table may be constructed:
______________________________________ Relative Relative i Compared to t t/(t - t) it/F i CXM at t = 0.95 ______________________________________ 0.95 2.71 1.00 1.00 1.57 0.85 3.40 1.25 1.40 2.20 0.75 5.00 1.84 2.33 3.67 0.65 13.00 4.79 7.00 11.00 ______________________________________
The last column shows that, comparing an AXM having t=0.95 with a CXM having t=0.95, C, C.sub.m, D and .delta. being the same, the current density at the AXM is 57% higher than in the case of a CXM. This means that the current density at an AXM can, in this case, be 57% higher before C.sub.m becomes negligible for practical purposes compared to C.sub.m. Column 3 (Relative it/F) shows that utilizing an AXM having t of 0.75 increases the relative transport of chloride ions (compared to t=0.95) by a factor of 1.84 (i.e. by 84%) whereas utilizing a CXM having t of 0.75 (compared to a CXM having t=0.95) resulted in an increase of sodium ion transport of only 24%. (Comparing an AXM having t=0.75 with a CXM having t=0.75, the transport of chloride ion compared to sodium ion at the same C, C.sub.m and .delta. is 57% greater).
The second exception of AXM compared to CXM arises as the voltage difference at the AXM-dilute solution interface approaches a few tenths of a volt. In this case hydroxide ions from the dissociation of water accompany the chloride ions passing from the diluting solution into the concentrating solution, an equal number of hydrogen ions passing from the interface into the diluting solution. The concentrate solution becomes alkaline and the dilute solution acidic. (The changes in alkalinity and acidity as measured by pH changes can be masked by the presence of carbon dioxide and/or bicarbonate which are pH change buffers). As the electric current is increased, in this case, the rate at which water dissociates becomes relatively large compared to the rate at which chloride ions are transferred and in fact most of the increase in current is carried by hydroxide ions passing into the concentrate solution. Therefore the changes in alkalinity and acidity can be quite large. The increase in alkalinity in the concentrate stream can result in precipitation of calcium carbonate on the concentrate side of the AXM if (as is frequently the case in "real" aqueous solutions) calcium bicarbonate is present. It is not that somehow the inherent rate of water dissociation has increased at an AXM but rather that AXM contain and/or have absorbed on their surfaces substances which catalyze the dissociation of water at the high voltage drops which exist at the AXM-dilute solution interface.
Examples are: ##STR1## In equations (4) the ##STR2## (benzyl dimethyl amine) groups result from the decomposition off ##STR3## (benzyl trimethyl ammonium) groups in the surface of the AXM. --COO.sup.-- (carboxylate groups) are present, for example, in the tannin like substances (generally called "humic" and "fulvic" acids) found in natural surface waters. Such tannin like substances are negatively charged and are transported (just like other anions) by the electric current to the AXM where they are strongly adsorbed, in part by multiple electrostatic attractions between positively charged groups ##STR4## in the membrane and negatively charged groups in the tannin like substance (--COO--). Colloidal metal oxides and hydroxides (e.g. iron hydroxide) present in water are also negatively charged and behave as weak acids. It is found that AXM, containing no amine groups (other than quaternary ammonium groups) and processing water free from tannin like substances and colloidal metal oxides and hydroxides, dissociate water in essentially the same amounts as CXM. Commercial CXM contain sulfonic acid groups (--SO.sub.2 H) which are strongly dissociated so that reaction (5a) does not take place, Most aqueous solutions do not contain positively charged organic or inorganic colloids so reactions similar to reaction (4) above do not generally occur from absorbed substances. It is possible however to make CXM which do catalyze water dissociation by incorporating in the CXM weakly basic and/or weakly acid groups. Whether in AXM or CXM, the most effective catalytic groups have ionization constants which are equal to the square root of the ionization constant of water (10.sup.-14), that is to 10.sup.-7. This may be seen by noting that 10.sup.-7 makes the rates of reactions (4b) and (4c) equal. It is possible to make AXM which do not have weakly basic (or weakly acid) groups and in which the bound positively charged anion exchange groups do not decompose into weakly basic (or weakly acid) groups. Such membranes, when processing clean water, will dissociate water only to the same extent as commercial sulfonate type CXM. Negatively charged organic and inorganic colloids may be removed by pretreatment of the solution with ultrafiltration or salt regenerated anion exchange with highly porous anion exchange resin granules.
The "actual area" of an AXM may be increased by filling the diluting space between the AXM and the adjacent CXM with anion exchange resin beads ("AXB"). Such filling can increase the limiting value of it/FC by an order of magnitude or more. (The limiting value of it/FC is that value at which for practical purposes C.sub.m, the concentration at the interface between the solution and the AXM (and the AXB), becomes negligible compared to C). The diluting space may be filled with AXB by pumping a dilute slurry of AXB into such diluting space or by filling the space with AXB before assembling the cell pair. (A "cell pair" consists of one AXM, one diluting space, one CXM and one concentrating space). Since water dissociation is most important at AXM (and AXB) there is merit in filling the diluting space solely with AXB. If it is desired to utilize both AXB and CXB granular resins in the diluting space then it is important to have as many AXB paths back to the AXM and CXB paths back to the CXM respectively, as possible. When the diluting space is filled before assembly of the cell pair such maximization of paths may be accomplished by spreading a layer of AXB on the AXM and then a layer of CXB on the AXB (or, of course, CXB on the CXM and AXB on the CXB). When the diluting space is filled by pumping, such maximization of paths may be accomplished by alternating dilute slurries of AXB and CXB, the resulting filled space then consisting of alternating layers of AXB and CXB (in the direction of fluid flow), each layer perhaps only a few beads thick. Alternatively the space between the AXM and CXM in the diluting space may be divided by a highly porous screen, expanded plastic sheet or diaphragm and AXB pumped in on the AXM side and CXB on the CXM side.
Even with such filling of the diluting space with ion exchange resin beads, it is still possible to arrive at current densities at which the concentration of salt at the membrane-dilute solution and bead-dilute solution interfaces approaches zero. If the current density is increased still further water will be dissociated at the solution-AXB and solution-AXM interfaces into hydroxide ions and hydrogen ions as discussed above. The hydrogen ions will enter the CXB and CXM along with other cations. Another, closely related, mechanism for water dissociation also exists which may be visualized by imagining a diluting space of zero thickness, i.e. the distance between the AXM and the CXM is zero. This is equivalent to a diluting space which is essentially instantly deionized and C.sub.m at the AXM-CXM interface approaches zero essentially instantly. When the voltage drop at such interface reaches a few tenths of a volt water will be dissociated at the AXM surface into hydroxide ions and hydrogen ions, the former ions passing through the AXM and the hydrogen ions through the CXM. (Such a zero thickness diluting space is called a "bipolar junction" and the pair of AXM and CXM with zero gap is called a "bipolar" membrane. Commercial bipolar membranes contain at the interface between the AXM and the CXM a thin layer of colloidal metal oxides and/or polymeric organic weak bases and/or weak acids to catalyze water splitting). A similar situation exists whenever there is an interface between AXM or AXB and CXM or CXB in which the AXM or AXB is generally on the anode (positive electrode) side of such interface (junction) and the voltage drop across such interface is several tenths of a volt. (If the AXM or AXB is generally on the cathode (negative electrode) side of such junction, then the junction acts like a zero gap concentrating space and very concentrated salt solution (e.g. 15%) will accumulate at the junction). There seem to have been no experiments to determine which water dissociation mechanism predominates at current densities much above the limiting it/FC, that is, which predominates: water dissociation (a) at AXM and/or AXB-solution interfaces or (b) at AXM and/or AXB junctions with CXM and/or CXB.
In commercial ED apparatus in which the diluting spaces are filled with IX resin beads, such beads seem always to have been a random mixture of equal gram-equivalents of AXB and CXB, that is about 60 parts of AXB to 40 parts CXB, apparently on the impression that such filled diluting spaces are an electrically regenerated mixed bed ion exchange deionizer. It is true that when the current density is far above that corresponding to the limiting it/CF (so that most of the electric current is carried by hydroxide and hydrogen ions) then the AXB and CXB will be largely in the hydroxide and hydrogen ion forms respectively. This may be proved by turning off the electric current whereupon solution passing through the filled diluting space will continue to be deionized (if the solution is dilute, then for some hours). However it is clear that when the dilute space is filled with a random mixture of IXB the objective is to maximize the number of AXB which are connected to the AXM and simultaneously the number of CXB which are connected to the CXM. If the AXB and the CXB have the same size such maxima clearly occurs (in a random mixture) when the volume (or number) ratio is 1:1. (Preferably the conductivities of the AXB and CXB will be the same under actual use conditions. The conductivities depend in known ways on the ionic form of the IXB, the water content and ion exchange capacity. Since the ionic form of the IXB may vary substantially from the entrance of a filled dilute space to the exit of such space, it may be preferred to vary continuously or step-wise the water content and IX capacity of the IXB from the entrance to the exit. It is also advantageous if one or both IXB are short-diffusion-path IXB ("SDP" or shell-and-core IXB), i.e. IXB in which the outer regions contain a normal concentration of groups and the inner regions contain a much lower (including zero) concentration). If the diameter of the beads is the same as the distance between the AXM and the CXM then all the beads are in contact with both membranes. For other ratios of bead diameter to AXM-CXM gap and for given ratios of number of AXB to CXB a computer program can be devised to calculate the number of AXB which are connected (through other AXB) to the AXM, the number of CXB connected to the CXM and the (harmonic) mean length of the AXB and CXB paths. *It may be possible to study such problem experimentally, for example by using a mixture of AXB and inert beads of the same diameter between a single pair of AXM, measuring the electrical resistance as a function of membrane gap and the ratio of the number of beads of each type. (It may also be possible to study the problem by using a mixture of copper beads and insulating glass or ceramic beads between a pair of copper plates).
It is generally accepted that whatever IXB are used, the diameters should all be the same. It is also clear that the surface area of IXB per cm.sup.3 of beads is inversely proportional to the diameter of the beads. The pressure drop per unit flow path length obviously also depends inversely upon bead diameter. IXB used for water softening or chemically regenerated deionization typically have diameters of about 0.05 cm. (Such typical bead size is obviously a compromise among practical pressure loss in an IX bed; duration of exhaustion run; and limiting exchange rate (i.e. avoiding control of such rate by diffusion in the IXB). Filled cell ED clearly involves a different compromise). Although such diameters (0.05 cm) have also been typically used in ED having diluting spaces filled with IXB, it is not clear that such diameters are optimum for ED. Very much smaller diameters are used for chromatographic analysis.
IXB are available in so called "gel" types in which the beads are transparent (but generally colored) and in "macroporous" ("macroreticular") types in which the beads are opaque. The gel types have water and IX groups more or less uniformly distributed throughout the bead. The (tortuous) pores typically have diameters of about 0.002 micrometer, varying however with the water content.
The macroporous types have comparatively large pores (e.g. 0.1 to 1 micrometer), the IX resin with its IX groups forming the walls of such pores. Diffusion in the large pores is very rapid. The water content of the resin of the pore walls is not generally reported though in principle it is measurable. The water content of the gel type IXB is generally varied by varying the amount of crosslinking monomer (for example divinyl benzene) used during suspension polymerization of the beads (for example from a mixture of styrene and divinyl benzene). The polymerized beads are treated with sulfuric acid to introduce sulfonic acid groups thereby producing CXB or with chloromethyl methyl ether and subsequently with a tertiary amine (e.g. trimethyl amine or hydroxyethyl dimethyl amine (also called dimethyl ethanol amine)) to introduce quaternary ammonium groups (e.g. ##STR5## Beads containing such IX groups swell when immersed in water, the loser the amount of crosslinking and the higher the concentration of IX groups the greater the amount of swelling. The most widely used gel type CXB are made from a mixture of styrene and 8% divinyl benzene (100% basis) although such CXB are also available commercially with 1 to 12% or more DVB. It has been shown that only about half the DVB in such beads is actually involved in crosslinking. However during polymerization as described above, the growing polymer chains become heavily entangled with each other, such entanglement also reducing swelling in water. The most widely used gel type AXB are made from a mixture of styrene and 6% divinyl benzene (100% basis) although such AXB are also available commercially with less or with more DVB. The same comments with respect to efficiency of use of DVB and entanglement apply also to AXB. In addition the treatment with chloromethyl methyl ether (chloromethylation) introduces some methylene crosslinks depending upon the treatment conditions e.g. the catalyst used. (It is also possible to introduce sulfone crosslinks in CXB, depending upon the method of sulfonation used). It is also possible to make gel type IXB by diluting the styrene and divinyl benzene with a non-polymerizable solvent such as diethyl benzene and using comparatively larger amounts of DVB. In such case the swelling of the IXB in water is determined by such solvent, the volume of water absorbed being essentially equal to the volume of solvent used. The efficiency of use of DVB is also roughly only 50% but the amount of polymer entanglement is not important.
In dilute solutions IXB generally prefer doubly charged ions (such as Ca.sup.++ and Mg.sup.++ or SO.sub.4.sup.=) to singly charged ions (such as Na.sup.+ respectively Cl.sup.- or NO.sub.3.sup.-) and triply charged ions (such as Sc.sup.+3 (scandium) or Fe(CN).sub.6.sup.-3 (ferricyanide anion)) to doubly charged ions. There is much confusion between "doubly charged" and "divalent" and between "triply charged" and "trivalent". Amphoteric metal hydroxides (that is metal hydroxides which can behave either as weak acids or weak bases such as cupric hydroxide, nickelous hydroxide, ferrous hydroxide, nickelic hydroxide, ferric hydroxide, aluminum hydroxide) have the same charge as their valence only in acid solutions (e.g. +2 for cupric, nickelous, ferrous, +3 for nickelic, ferric and aluminum). The alkaline earth cations (Mg.sup.+2, Ca.sup.+2, Sr.sup.+2, Ba.sup.+2) are divalent and doubly charged in essentially neutral solutions and the rare earth cations (including Sc.sup.+3 (scandium cation) and La.sup.+3 (lanthanum cation) are trivalent and triply charged in essentially neutral solution. The preference for multiply charged ions compared to singly charged ions may be illustrated by the following reaction:
(6) Ca.sub.s.sup.++ +2Na.sub.r.sup.+ .fwdarw.Ca.sup.++.sub.r +2Na.sub.s +where the subscript "s" refers to solution and the subscript "r" refers to the CXB resin phase. One can write an equilibrium constant:
(7) ##EQU8## where the quantities in parentheses are expressed in gram-moles per kilogram of water (or, what is the same, milligram-moles per gram of water). The equation may be rearranged to: ##EQU9## where K ##EQU10## is defined as "Y" (not a constant) for ease in manipulation. The ion exchange capacity of the CXB in gram-equivalents per kilogram water (i.e. the molality) is given by: EQU Q=2(Ca.sub.r.sup.++)+(Na.sub.r.sup.+). (9)
Then ##EQU11## This is a quadratic equation which has the solution: ##EQU12## For example if Y is 250 (liters/mole), corresponding for example to K=1, Ca.sub.s.sup.++ =40 ppm and Na.sub.s.sup.+ =46 ppm, then the following table may be constructed:
______________________________________ Q 2 Ca.sub.r.sup.++ /Q % H.sub.2 O ______________________________________ 0.1 0.87 97 1.0 0.96 78 10 0.99 26 ______________________________________
The second column (2Ca.sub.r.sup.++ /Q) is the fraction of the CXB which is in the Ca.sup.++ form, the remainder being in the Na.sup.+ form. The third column (%H.sub.2 O) is the percent by weight of water in a CXB having a dry weight capacity of 3.5 milligram equivalents per gram of dry CXB, a typical value. The effect of Y (defined as K ##EQU13## may be seen by setting Y=25 l/mol (consistent with K=1, Ca.sub.s.sup.++ =400 ppm, (Na.sup.+).sub.s =460 ppm) from which the following table may be constructed:
______________________________________ Q 2 Ca.sub.r .sup.++ /Q % H.sub.2 O ______________________________________ 0.1 0.64 97 1.0 0.87 78 10 0.96 26 ______________________________________
Although the ratio of Ca.sup.++ to Na.sup.+ in solution in the latter table is the same as in the former table, this total concentration in solution is 10 times greater in the latter table resulting in loss of preference for Ca.sup.++ compared to Na.sup.+ in the CXB. K for Ca.sup.++ and Na.sup.+ is not exactly 1 and in addition K is not exactly constant. Nevertheless the above simple calculation illustrates the principles involved. The conductivity per ion (equivalent conductivity) in the case of the CXB having only 26% water is very much less than that having 97% water (the latter having an ion conductivity essentially the same as that of water) because of friction between the ions and the polymer of the CXB in the former case (low water content) and the necessity of ions to follow a tortuous path through such resin. The ratio of the conductivity of Ca.sup.++ ion to Na.sup.+ ion is less in the CXB having 26% water than in that having 97% water, in part because of the electrostatic attraction of the doubly charged ion for the fixed sulfonic acid groups. Nevertheless, in ED without filling in the diluting spaces or with filling in which the CXB portion is prepared from styrene-divinyl-benzene mixtures having 8% DVB, Ca.sup.++ is generally preferentially removed compared to Na.sup.+, at least at current densities such that C.sub.m (the total concentration at the CXM and/or CXB solution interface) is not far removed from C (the concentration outside the laminar flow layer adjacent to the CXM or CXB).
Similar considerations apply to the comparative absorption and conductivity of doubly charged sulfate anions compared to singly charged chloride anions or nitrate anions in AXM or AXB. (K for nitrate ions compared to chloride ions is about 2 for most AXM or AXB). However it appears that bulky quaternary ammonium groups such as ##STR6## (benzyl tributyl ammonium) exclude sulfate compared to chloride (or nitrate) as compared with the common commercial quaternary group ##STR7## (benzyl trimethyl ammonium). Such exclusion appears to be due in part to the lack of ability of the doubly charged sulfate ion to approach closely the positively charged nitrogen atom.
The electrodialytic performance of IXM and IXB is however not determined solely by the equilibrium absorption of ions by the IXM or IXB or by the relative conductivities of the ions in the membranes or beads. It is possible to make thin skins on the surfaces of IXM and IXB which skins retard the passage of doubly and triply charged ions. (The skins have low ion exchange capacities, low water contents and low dielectric constants). Such membranes are called "univalent ion selective membranes" and are typically used to prepare 18 to 20% sodium chloride brine by ED from sea water, permitting the passage of sodium and chloride ions and inhibiting the passage of magnesium, calcium and sulfate ions. (The use of the term "univalent ion selective" is not accurate; it would be better to say "selective for singly charged ions" but since the membranes are almost always used to separate ions which have the same charge as their valency (but what is the "valency" of sulfate?) there is no practical harm in the former term). In the above concentration of seawater by ED using such skinned membranes, the current density used is far less (e.g. 50% or less) than that corresponding to the "i" in the limiting value of it/FC (that is to the "i" at which C.sub.m is negligible compared to C, the bulk concentration in the diluting space). At or above the limiting it/FC what goes through a membrane is essentially what is presented to the membrane by diffusion and conduction in the laminar flow layer adjacent to the membrane. The ratio of the ions arriving at the membrane is the ratio of the limiting it/FC that is the ratio ##EQU14## Univalent anion selective membranes have been used selectively to remove nitrate from water containing also sulfate and/or bicarbonate or (with CXM which are not univalent ion selective) selectively to remove calcium chloride from water containing sodium, calcium, chloride, sulfate and bicarbonate ions. In each case the it/FC actually used is 50% or less than the limiting it/FC.
It was noted above that the ratio of the conductivity of doubly charged ions compared to singly charged ions is less in IXB having low water contents than in IXB having high water contents, in part because of the electrostatic attraction of the doubly charged ions for the fixed (singly charged) ion exchange groups. It was also pointed out that bulky, quaternary ammonium anion exchange groups tend to exclude doubly charged sulfate ions in part due to the inability of the doubly charged ions to approach closely the positively charged nitrogen atom in the quaternary ammonium exchange group. One might therefore expect that such diminished electrostatic attraction would lead to greater conductance per sulfate ion at the same water content and same AXB molality (gram-equivalents of fixed, anion exchange groups per kilogram of water in the AXB). A recent report seems to confirm that sulfate is more mobile in an AXB having ##STR8## AX groups than in an AXB having ##STR9## groups.
Sulfate mobility may be even higher in AXB having ##STR10## (benzyl tributyl ammonium) groups. However, as noted above, the latter groups highly exclude sulfate and therefore the relative transport of sulfate versus chloride from solutions containing both ions (at it/FC substantially less than the limiting it/FC) may be poor even though the sulfate ion mobility is comparatively high. It would appear that "pleasingly plump" (rather than "bulky") groups are indicated. In addition to (CH.sub.3).sub.2 N.sup.+ CH.sub.2 CH.sub.2 OH groups, these may include: ##STR11## Commercial AXB are available having N.sup.+ CH.sub.2 CH.sub.3).sub.3 groups. Such AXB appear to be macroporous and it is not known whether sulfate mobility will be the same in a macroporous AXB having such groups as compared to a gel type AXB with such groups.
All commercial ED apparatus having IXB in the diluting spaces use a mixture of AXB and CXB. All such apparatus use as CXB gel type beads having ##STR12## as the exchange groups, known for example as Dowex 50 (Dow Chemical Co.) or Amberlite IR120 (Rohm and Haas Co.). Most such apparatus use as AXB gel type beads having ##STR13## exchange groups (known as Type I groups) for example Dowex 1 or Amberlite IRA 400. The remaining commercial apparatus used (at least originally) AXB gel type beads having ##STR14## exchange groups (known as Type II groups) for example Dowex 2 or Amberlite IRA 410. In the 1960's, an in-house apparatus used a macroporous (macroreticular) AXB having Type I AX groups (Dowex 21K was actually used; similar AXB are available from other manufacturers) to supply deionized water for laboratory use.
(Macroporous (macroreticular) IXB are made, for example, from a mixture of styrene and divinyl benzene with a diluent which is a solvent for the styrene and DVB and a poor solvent for the polymer of styrene and DVB. As a result, as polymerization proceeds the polymer precipitates from solution leaving macropores. The size of the macropores depends upon the quantity of the diluent and its solubility for the polymer. A diluent may be used consisting of a mixture of a good solvent for the polymer and a poor solvent. The amount of DVB used may be the same as used in gel type IXB or less because the polymer in macroporous IXB tends to be highly entangled, the extent depending on the diluent used. With some polymeric diluents it is possible to use no DVB).
Almost all of the above discussion has pertained to the diluting space in an ED apparatus. The design of the concentrating space cannot, however, be neglected. The concentrating space should contain structure to keep the adjacent IXM flat and against whatever structure (turbulence promoting spacer or IXB) may be present in the adjacent diluting spaces. The structure in the concentrating space should also assist the adjacent IXM to resist whatever hydraulic pressure difference there may be from the diluting side of the membranes to the concentrating side. (It is common to operate the diluting space at a higher pressure than the concentrating space in order to avoid possible leaks of concentrate solution into the dilute solution). The concentrating space may be identical in structure to the diluting space e.g. have the same thickness, the same turbulence promoting structure or the same IXB. In such case the choice of which electrode of the pair (discussed above) is positive and which is negative is arbitrary. If the solution processed in the diluting space contains organic or inorganic colloidal matter and/or poorly soluble salts, then the colloidal matter can accumulate at one or the other of the diluting surfaces of the IXM and/or IXB and the poorly soluble salts at one or the other of the concentrating surfaces of the IXM and/or IXB. Regular, periodic reversal of the polarity of the electrodes will then convert a diluting space into a concentrating space and a concentrating space into a diluting space, generally effectively removing accumulated colloids and poorly soluble salts. Cycle times of 30 minutes to 2 weeks are used commercially depending upon the severity of accumulation of colloids and poorly soluble salts (that is reversing polarity every 15 minutes to one week). It is not necessary that such reversal be symmetric (that is, that each space spend equal time as a diluting space and a concentrating space). It is equally possible to operate very asymmetrically say 15 minutes in one direction and 15 seconds in the other. In the case of substantially symmetric reversal whatever structure is optimal for diluting and concentrating spaces in one direction is obviously also optimal in the opposite direction and therefore the structure (e.g. non-woven screen or IXB) should be the same in both spaces. In the case of asymmetric or no reversal the structure in the two types of spaces need not be the same. For example the distance between the AXM and the CXM in the concentrating space can be very much less than such distance in the diluting space and such thin concentrating space can have structure enabling a single pass of concentrate solution through the concentrating space without recycle (nevertheless at a pressure loss which is only slightly less than that in the diluting space) thereby avoiding the investment and operating cost of concentrate solution recycle. A single pump can be used to feed both concentrating and diluting spaces while still maintaining the desired ratio of effluent flows (i.e. percent of feed which is recovered as deionized product). Instead of (or in addition to) using concentrating spaces which are thinner than the diluting spaces (to eliminate the need for recycle of concentrate) it is possible to fill the concentrate space with IXB having a smaller mesh size (smaller diameter) than the IXB used in the diluting spaces, the smaller diameter resulting in greater hydraulic resistance. Of course attention must be paid to achieving the necessary .delta. in the concentrating space to assure adequate mass transfer of poorly soluble electrolytes (e.g. silicic acid (silica), calcium bicarbonate and calcium sulfate) from the interfaces between the IXM (and IXB, if such are used in the concentrating space) and the concentrating solution into the bulk of such solution.
If the diluting solution being deionized is already very dilute (e.g. 6 ppm as sodium chloride) then, even at 90% recovery of deionized dilute solution the conductivity of the concentrating solution effluent will be only about 100 micro Siemens/cm. If in such case IXB filling is used in the diluting space (which will be highly desirable to increase the effective current density in the diluting space and to decrease the electrical resistance of such space), then the principal electrical resistance of the cell pair will be in the concentrating space and it will be desirable to use IXB filling also in the latter space. Such IXB filling need not be the same as the filling in the diluting space. For example in the above mentioned filled cell ED apparatus used in-house in the 1960's, it was found advantageous to fill the concentrating spaces solely with weak base AXB.
The above discussion has concentrated on the use of IXB as filling in the diluting and/or concentrating spaces. The literature also reports apparatus in which the surface of AXM was corrugated at an angle of 45.degree. to the direction of flow, the CXM corrugated at -45.degree. and the corrugations of the AXM were in contact with those of the CXM. The flow was thereby forced to make frequent 90.degree. changes in direction. Apparatus is also reported in which AX fabric was placed against the AXM in the diluting space and CX fabric against the CXM in the same space. The fabrics were knit from IX fibers. CX fibers are most easily made from polyethylene mono- or multi-filaments by soaking the latter in a mixture of styrene, divinyl benzene and free radical catalyst, polymerizing the monomers and subsequently sulfonating. AX fibers may be made by substituting vinyl benzyl chloride for the styrene and finally treating the filaments with an appropriate tertiary amine as discussed above. (IX fibers and filaments may also be made by sulfo-chlorinating polyethylene fibers and filaments, subsequently hydrolyzing or aminating and quaternizing). Such IX monofilaments may be easily bonded together by moderate heat and pressure to give non-woven screens. The latter can obviously be made on automatic machinery. The literature reports that the highest values of limiting it/FC were obtained when there was some interpenetration of the AX knitted fabric with the CX knitted fabric. IX monofilaments or multifilaments having a diameter equal to the spacing between the AXM and the CXM may also be arranged in alternation parallel to the direction of flow.
In the above discussion limiting values of it/FC were used as the basis of discussion since such ratio reflects the actual transfer of ions ##EQU15## In engineering practice it is common to use the ratio ##EQU16## because it relates the easily measurable i and C. It does not however relate to the performance of the ED apparatus.